Option Pricing in the Approach of Integrating Market Risk Premium: Application to OTM Options

Abstract

In this research, we summarize the results of implementing the market risk premium into the option valuation formulas of the Black–Scholes–Merton model for out-of-the-money (OTM) options. We show that derivative prices can partly depend on systematic market risk, which the BSM model ignores by construction. Specifically, empirical studies are conducted using 50ETF options obtained from the Shanghai Stock Exchange, covering the periods from January 2018 to September 2022 and from December 2023 to October 2025. The pricing of the OTM options shows that the adjusted BSM formulas exhibit better pricing performance compared with the market prices of the OTM options tested. Furthermore, a framework for the empirical analysis of option prices based on the Capital Asset Pricing Model (CAPM) or factor models is discussed, which may lead to option formulas using non-homogeneous heat equations. The later proposal requires further statistical testing using real market data but offers an alternative to the existing risk-neutral valuation of options.